2010-11-17
Finally: Rotations of real Spherical Harmonics according to Blanco et al.
I finally managed to implement Blanco's 1997 paper. The formulas were quite tedious to implement correctly, with all the matrix indices going possibly wrong. But after lots of debugging, I now have a working implementation in my SH explorer. Have a look:
This is an antenna pattern by Tiiti, which was rotated by 45, 90 and 45 degrees, in ZYZ angles. And it did not explode or deform badly. :)
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nice! how robust is this? the total energy should be conserved as it's stored in the first basis, but what about the other bands. The bands themselves are probably energy conserving, too (just a wild guess), but how bad is the numerical error after a few rotations?
ReplyDeleteI still have to test robustness. On first glance it seems fairly robust. Lucky enough, I do not need consecutive rotations, which I guess should help with numerical stability. Will report on that when I know more.
ReplyDeleteI guess I can compute the norm of the band vectors or just an approximate integral of the reconstructed function.